Physics H



Physics H Name ____________________________ Per ____

Math Skills I

1. What is the difference between units, dimensions and measurement?

2. What are the seven fundamental dimensions and their corresponding units in the SI system?

3. Give four examples of derived dimensions and their corresponding SI units.

Identify the unit, dimension and measurement in the following statements:

Dimension Unit Measurement

“The mass of the object is 7.52 x 102 kg.” ______________________________________

“Silver has a density of 10.5 g/cm3.” ______________________________________

Using Units: (p. 959 in your text)

List the quantity measured and the conversion for each:

Hertz

Joule

Newton

Volt

Complete the following table:

Dimension SI unit ____cgs unit __________Common (B/E) unit_

Mass (M) __________ _________ ___________

___________ s _________ ___________

___________ __________ _________ ft

___________ __________ cm3 ___________

Show work with correct units:

A back yard is 5.9 m long and 7.5 m wide.

a) What length of fence will enclose the yard?

b) How much sod will cover the yard?

Units will help you work this problem:

A wooden block has dimensions of 2.0 cm x 30 mm x 4.0 x 10-2 m.

It has a density of 0.60 g/cm3

a) What is the area of the largest face?

b) What is the volume of the block?

c) What is the mass of the block of wood?

d) What is the mass in kg?

DIMENSIONAL CONSISTENCY

Any valid formula must be “dimensionally consistent”. That is, each side of the equal sign must have the same unit. For example: Given [pic] where x is in meters, v is in meters per second and t is in seconds.

Replacing the variables with the units symbol produces m = m + (m/s)s. The “s” cancels leaving m = m + m which has m on both sides and is dimensionally consistent.

1. [pic] where x is in meters, v in meters per second, t in second and

a (acceleration) in meters per second squared.

2. The time [pic]required for one complete oscillation of a mass [pic]on a spring of force constant

[pic] is: [pic] . Find the dimensions [pic] must have for this equation to be

dimensionally correct.

Physics H Name ____________________________ Per ____

Math Skills II

Convert each value to the unit indicated: show your work (on back or separate paper)

1) 30 mi/hr _________ m/s 6) 1.0 yr ______________ s

2) 70 mi/hr _________ m/s 7) 1.0 m2 ______________ cm2

3) 25 m/s _________ km/hr 8) 30 mi/hr ______________ ft/s

4) 4.8 g/cm3 _________ kg/m3 9) 2.10 x 10-7 s _______________ ns

5) 35 km _________ mm 10) 1.753 x 10-13 s _____________ ps

Significant Figures (sig figs):

Express the measurement 4.29478416 kg with 8, 6, 4, and 2 significant figures.

Round off the following numbers to one sig fig.

a. 3.7 × 105 ____________ d. 0.000067 ____________

b. 6.1 × 105 ____________ e. 7439262 ____________

c. 8.2 × 10–9 ____________ f. 0.0006739 ____________

According to the rules given in Chapter 1 of your textbook, how many significant figures are there in the following measurements?

a. 0.0845 kg ____

b. 37.00 h ____

d. 0.000 000 0217 g ____

e. 750 in.

c. 8 630 000.000 mi ____ f. 0.5003 s ____

Use scientific notation and do the following calculations (watch those units):

1) 30 x 0.0002 / 60000

2) 5.0 x 10-15 kg - 2.0 x 10-15 kg =

3) (5.3 x 10-5 m) (3.9 x 1012 s) =

4) 3 x 10-4 s =

9. x 10-8 s

5) (5 x 10-9 kg) (4 x 109 m) =

( 8 x 105 s)

6) 6.4 x 10-5 m2 - 2.6 x 10-6 m2 =

Complete the following chart regarding metric prefixes. Use scientific notation:

Given unit remove prefix change unit_____

1. 20 mm ___________________ m __________________ km

2. 13 μm ___________________ m __________________ pm

3. 270 nm ___________________ m __________________ cm

4. 2.0 Mg ___________________ g __________________ kg

5. 99 Ts ___________________ s __________________ Gs

The radius of a circle is 5.5 cm,

a. What is the circumference in meters?

b. What is its area in square meters?

Physics H Name ____________________________ Per ____

Math Skills III

EQUATIONS (algebraic manipulation)

[pic]Often Physics problems are done with variables only. Solve each equation for the variable indicated. Show ALL your work leading to the answer.

K = [pic]kx2 solve for x:

T = 2π [pic] solve for g:

[pic] solve for v:

[pic] solve for di:

[pic] solve for B:

v2 = v02 + 2a(s – so) solve for a:

GEOMETRY/TRIGONOMETRY

Using right triangle trigonometry and the Pythagorean Theorem solve the following. Your calculator must be in degree mode. SHOW ALL YOUR WORK! Remember: SOH CAH TOA

sin θ = opp / hyp cos θ = adj / hyp tan θ = opp / adj

[pic]

a. θ = 55o and c = 32 m, solve for a and b.

b. θ = 45o and a = 15 m/s, solve for b and c.

c. b = 17.8 m and θ = 65o, solve for a and c.

Line B touches the circle at a single point. Line A extends through the center of the circle.

a. What is line B in reference to the circle?

__________________________

b. How large is the angle between lines A and B?

_______________

What is angle C? _____

What is angle θ ? _____

What is angle Φ? _____

GRAPHING

Frequently an investigation will involve finding out how changing one quantity affects the value of another. The quantity that is deliberately manipulated is called the independent variable. The quantity that changes as a result of the independent variable is called the dependent variable.

The relationship between the independent and dependent variables may not be obvious from simply looking at the written data. However, if one quantity is plotted against the other, the resulting graph gives evidence of what sort of relationship, if any, exists between the variables. When plotting a graph, take the following steps.

1. Identify the independent and dependent variables.

2. Choose your scale carefully. Make your graph as large as possible by spreading out the data on each axis. Let each space stand for a convenient amount. For example, choosing three spaces equal to ten is not convenient because each space does not divide evenly into ten. Choosing five spaces equal to ten would be better. Each axis must show the numbers you have chosen as your scale. However, to avoid a cluttered appearance, you do not need to number every space.

3. All graphs do not go through the origin (0,0). Think about your experiment and decide if the data would logically include a (0,0) point. For example, if a cart is at rest when you start the timer, then your graph of speed versus time would go through the origin. If the cart is already in motion when you start the timer, your graph will not go through the origin.

4. Plot the independent variable on the horizontal (x) axis and the dependent variable on the vertical (y) axis. Plot each data point. Darken the data points.

5. If the data points appear to lie roughly in a straight line, draw the best straight line you can with a ruler and a sharp pencil. Have the line go through as many points as possible with approximately the same number of points above the line as below. Never connect the dots. If the points do not form a straight line, draw the best smooth curve possible.

6. Title your graph. The title should dearly state the purpose of the graph and include the independent and dependent variables.

7. Label each axis with the name of the variable and the unit. Using a ruler, darken the lines representing each axis.

The graph shown below was prepared using good graphing techniques.

Go back and check each of the items mentioned above.

[pic].

Graph the following sets of data using proper graphing techniques.

The first column refers to the y-axis and the second column to the x-axis

1.

|Volume (mL) |Pressure |

| |(torr) |

|800 |100 |

|400 |200 |

|200 |400 |

|133 |600 |

|114 |700 |

|100 |800 |

|80 |1000 |

[pic]

2.

|Position (m) |Time (s) |

|0 |0 |

|5 |1 |

|20 |2 |

|45 |3 |

|80 |4 |

|125 |5 |

[pic]

|Speed (m/s) |Time (s) |

|0 |0 |

|20 |1 |

|45 |2 |

|60 |3 |

|84 |4 |

|105 |5 |

3.

[pic]

INTERPRETING GRAPHS

In laboratory investigations, you generally control one variable and measure the effect it has on another variable while you hold all other factors constant. For example, you might vary the force on a cart and measure its acceleration while you keep the mass of the cart constant. After the data are collected, you then make a graph of acceleration versus force, using the techniques for good graphing. The graph gives you a better understanding of the relationship between the two variables.

There are three relationships that occur frequently in physics:

[pic]

Graph A: If the dependent variable varies directly with the independent variable, the graph will

be a straight line (linear)

Graph B: If y varies inversely with x, the graph will be a hyperbola. (inverse)

Graph C. If y varies directly with the square of x, the graph is a parabola. (exponential)

Reading from the graph between data points is called interpolation. Reading from the graph beyond the limits of your experimentally determined data points is called extrapolation. Extrapolation must be used with caution because you cannot be sure that the relationship between the variables remains the same beyond the limits of your investigation.

1. Suppose you recorded the following data during a study of the relationship of force and acceleration. Prepare a graph showing these data.

|Force |Acceleration |

|(N) |(m/s2) |

|10 |6.0 |

|20 |12.5 |

|30 |19.0 |

|40 |25.0 |

[pic]

a. Describe the relationship between force and acceleration as shown by the graph.

b. What is the slope of the graph? Remember to include units with your slope. (1 N: 1 kg.m/s2)

c. What physical quantity does the slope represent?

d. Write an equation for the line.

e. What is the value of the force for an acceleration of 15 m/s2?

f. What is the acceleration when the force is 50.0 N?

2. The following data show the distance an object travels in certain time periods. Prepare a graph showing these data.

|Position (m) |Time (s) |

|0 |0 |

|2 |1 |

|8 |2 |

|18 |3 |

|32 |4 |

|50 |5 |

[pic]

a. Describe the relationship between x and y and write a general equation for the curve.

b. Is the distance traveled greater between 0 s and 1 s or 3 s and 4 s?

c. Is the slope of the curve greater between 1 s and 2 s or 3 s and 4 s?

-----------------------

(

30o

bÁíÁîÁôÁõÁúÁ |ÂÂ

Â

ÂÂ@ÂC”ÂêØÀ«–À«–}–cNB*ê/hmtËhmtË5?B*[pic]CJOJQJ\?^JaJphhmtËCJOJQJaJ)hmtËhmtËB*[pic]CJOJ |QJ |^J |aJph2j-ÈhmtËhmtËB*[pic]CJOJ |QJ |U[pic]^J |aJph0hmtËh˜6‡B*[pic]CJEHH*[pic]OJ

QJ

^J

aJph)hmtËh˜6‡B*[pic]CJOJ

QJ

^J

aJph)hmtËh˜6‡B*[pic]CJOJ

QJ

^J

aJph/hmtËh˜6‡5?B*[pic]CJOJ

QJ

\?^J

aJph#hmtËBΦ

45o

30o

C

A

B

30o

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download